Police should not be routinely armed, Theresa May has said in the wake of the "savage" killing of two female officers.

The home secretary cut short her holiday to return to the UK to visit the headquarters of Greater Manchester police on Wednesday. May was given a two-hour briefing by senior officers conducting the investigation into the double murder of their own colleagues, which she described as "savage acts of pure brutality".

Constables Nicola Hughes, 23, and Fiona Bone, 32, died in a gun and grenade attack on Tuesday morning after being lured to a house on the Hattersley estate, Tameside, on a routine call. Shortly afterwards Dale Cregan, from Droylsden, walked into Hyde police station nearby, where he was arrested on suspicion of the officers' murders. The 29-year-old had been the subject of a huge manhunt following the murders of a father and son in separate attacks in the area earlier this year.

The home secretary pledged to support police in their investigation but again stated that government policy was against the routine arming of officers.

"The Home Office have been supporting Greater Manchester police in the work that they've been doing in relation to this case over the past week and will continue to do so," she said.

"I'm clear that every resource that GMP needs should be made available to it and forces across the country have been giving support in the work that GMP are doing.

"I think we are clear we have a British model of policing that is one that our police very much support.

"I think that routine unarmed policing that goes on in our streets is right. I don't think this is the time to be calling for the arming of police."

After the deaths, Nick Clegg also warned against arming police. "I don't think this is the time to rush to instant judgments; this really is a time for mourning and support, of course, for the family and friends of the two women who have been killed," the deputy prime minister said.

May paid tribute to the "brave and talented" officers who were gunned down.

"These were brave and talented officers who were going about their everyday duties, doing what they do, day in, day out, protecting the public, fighting crime and they were incredibly brave and their deaths are a reminder of what police officers face every day."

May met Sir Peter Fahy, chief constable of Greater Manchester police, who said his force was still "under threat" following the murder, with a cache of grenades still possibly in the hands of criminal gangs.

Fahy said: "We are not confident that we have recovered all the grenades, we don't know for certain, so we've made it clear to our officers that the threat is still there."

He said the force's main priority had been supporting their families "who clearly have a huge amount to come to terms with".

Witnesses said a hail of bullets was fired before the grenade was used during the attack.

Thousands of tributes poured in for the fallen officers, including one from the Queen, and the force held a minute's silence at 11am on Wednesday, almost exactly 24 hours after the attack.